Modulational stability of ground states to nonlinear Kirchhoff equations

We investigate the stability of ground states to a nonlinear focusing Schr\"odinger equation in presence of a Kirchhoff term. Through a spectral analysis of the linearized operator about ground states, we show a modulation stability estimate of ground states in the spirit of one due to Weinstein {\it SIAM J. Math. Anal.}, 16(1985),472-491.